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We investigate the 2-flavor QCD with non-degenerate quark masses atlow-energy, using the chiral perturbation theory including the $\eta$ meson andanomaly effects. For the fixed $m_d\not=0$, the neutral pion becomes masslessat two values of $m_u$, between which a spontaneously CP broken phase appearswith the neutral pion condensation. We then show that the topologicalsusceptibility diverges at these two critical points. We also consider the caseof $m_u=m_d$ but $\theta=\pi$, equivalently $m_u= - m_d$ with $\theta = 0$ bythe chiral rotation and show that the CP symmetry is spontaneously broken bythe $\eta$ condensation at small $m$. Around $m=0$, three pions becomeNambu-Goldstone modes, showing non-standard behavior that $m_\pi^2 = O(m^2)$,which, however, is consistent with the chiral Ward-Takahashi identities.}

Pion masses in 2-flavor QCD with $\eta$ condensation